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CANCUN, Mexico (CNN) -- Hurricane Wilma was "relentlessly pounding" Mexico's Yucatan Peninsula early Saturday, the National Hurricane Center said, packing 125 mph winds and dumping "tremendous" amounts of rain that may not let up in the popular tourist area for the next 24 hours.

The tourist destination took a fierce battering as the center of the Category 3 storm passed directly over Cozumel Island before making landfall near Playa de Carmen, south of Cancun.

A CNN crew in Cancun recorded a wind gust of 150 mph, and the combination of wind and rain reduced visibility to near zero. The roaring winds were strong enough to bend trees and a traffic light completely over and shear the covering off of the roof of a nightclub.(Watch Wilma batter Cancun -- 1:45)

The storm surge in Cancun was forecast to reach 11 feet.

Forecasters said that because of the slow speed of the storm, 10 to 20 inches of rain could fall in the Yucatan and western Cuba -- and more than 3 feet of rain was possible in some isolated areas. Over a six-hour period Friday night, the storm moved just 18 miles.

Wilma is projected to creep up the Yucatan coast, cross the tip of the peninsula and then take a turn to the northeast and head toward western Cuba and Florida.

More than 20,000 tourists in Yucatan resorts were ordered out of their beachfront hotels, and those who could not find transportation out of the area were evacuated to shelters. Because many houses in the region are made of concrete, some residents chose to ride out the storm in their homes.

"It feels like the entire house is shaking. It's pretty intense," said Kimberly Howell, a Cancun resident, as the outer eye wall of the storm moved over the city. "I'm hearing a lot of glass breaking and a lot of loud banging sounds."

New Jersey resident Michael Attardi said he and his father-in-law were among as many as 100 Americans holed up at Hotel Cozumel. Winds were breaking windows in the lobby and sending water into the hotel, about 60 yards from the ocean.

"We have the children and the women in a separate bunker," he said. "The men are here, all trying to just keep the actual water out of the area here."

Streets were flooded with water 3 to 4 inches deep, and electricity was out, he said.

Wilma's slow dance in the Yucatan may be good news for Florida, where the center of the storm is expected to hit Monday afternoon. By then, the storm is predicted to be downgraded to a Category 1 or 2, with winds between 74 mph and 110 mph.

"But it's still going to be a hurricane," National Hurricane Director Max Mayfield warned. "A Category 1 or Category 2 hurricane can still have a significant impact."

He said that landfall is expected along the southwest Florida coast, south of Tampa. However, computer models of the storm's path differ widely on how fast Wilma will move, so "people really need to pay attention to the forecast," he said.

Cuban evacuations

Wilma approached Mexico with about the same strength as Hurricane Katrina, a Category 4 storm that slammed into Louisiana August 29, killing more than 1,200 people.

While the current forecast doesn't show Wilma making landfall in Cuba, the storm's center is expected to near the country's western tip Monday en route to south Florida.

Portions of the western Cuba could see more than 3 feet of rain.

A tropical storm warning was in effect for Cuba's provinces of Pinar del Rio, Havana and the Isle of Youth on Friday evening. The area west of Matanzas province through Pinar del Rio and the Isle of Youth was under a hurricane watch.

As the outer bands of the 400-mile-wide storm pounded Cuba, its government was evacuating more than 300,000 residents from the western provinces alone. In all, about half a million people are expected to have evacuated, and most will be taken to Havana. (See video on Cuba's preparedness -- 2:09)

Early Friday, data from Cuba indicated that 20-foot waves were pounding portions of the southern coast of Cuba's Isle of Youth, the hurricane center said.

FEMA, Florida prepare

Watches and warnings probably will be posted for Florida beginning Saturday.

In the Florida Keys, a mandatory evacuation begins at 6 a.m. Saturday for mobile home residents; the evacuation for people with special needs will follow later in the morning, and a general evacuation of the remaining residents begins Saturday afternoon.(Full story)

Mayfield, of the National Hurricane Center, said that tropical storm force winds of at least 39 mph will begin affecting the southernmost Florida Keys late Sunday or early Monday.

In Collier County, Florida, a mandatory evacuation began Friday for residents south and west of U.S. 41 and will continue until Sunday morning. An evacuation of barrier islands and mobile home residents in Lee County, Florida, begins at noon Saturday.

About 100 people already have taken refuge in a shelter set up at Florida International University in Miami, said Billy Wagner, director of the Monroe County Emergency Management Department.

U.S. Federal Emergency Management Agency acting director David Paulison said Friday hundreds of satellite telephones are being delivered to local officials in Florida in case communication lines are destroyed. He said FEMA is preparing for a major hurricane.

"We are going to have situational awareness over this storm to make sure that we know what's going on and we can provide the equipment and the supplies that that particular community needs," Paulison said.

Hurricane Katrina wiped out all means of communication in Louisiana and parts of Mississippi when it hit in August, isolating several communities for days and hampering rescue efforts in New Orleans.